**Today's science is tomorrow's technology.**

The 15th day of the year; 15 is the maximum number of pieces that can be produced from a cylindrical cake with four planar slices. These are called "cake numbers" and the first four are 2, 4, 8, and 15. What comes next?

The 15 digit word "Saippuakauppias" is Finnish for "soap dealer," and one of the longest single-word palindromes in everyday use. *Cliff Pickover @pickover (This is the longest single word palindrome in the world that is in everyday use) (The English word tattarrattat, the longest palindrome in the Oxford English Dictionary, was coined by James Joyce in Ulysses for a knock on the door)

The Fifteen Puzzle was the Rubick's Cube of it's day. Popularized (but not invented) by American puzzle master Sam Loyd. Get your own

or read the story here, from a modern day puzzle master,

**EVENTS**

**1559**Queen Elizabeth entered Westminster Abbey in her coronation robes, cloth and gold trimmed in Ermin. In the Abbey to witness the procession was the mathematician John Dee, who had selected the date for the coronation according to his horoscope reading. A big step up for the man who had been arrested on 28 May, 1555 by Elizabeth's sister, Queen Mary, to be held and questioned on charges of conjuring and heresy. *Benjamin Wooley, The Queen's Conjuror

"Dee's biographers usually state that he chose Elizabeth's coronation date, but the Council seems to have settled on 15 January even before Dee's return to favour. Against the occult threats facing the new Queen, Dee performed a greater service at Dudley's suggestion, delivering an electionary horoscope about the day 'appointed for her Majesty to be crowned in'. […] However, Dee's electionary horoscope, based on Ptolomy and his numerous Arabic and medieval followers, did not 'elect' a time for Elizabeth's coronation but interpreted the horoscope governing her coronation day. "

*Glyn Parry, The Arch-Conjuror of England: John Dee, Yale University Press, New Haven & London, 2011, p 49 via Thony Christie

**1759**, the British Museum, in Bloomsbury, London, the world's oldest public national museum, opened to the public who were admitted in small groups, by ticket obtained in advance, for a conducted tour. It was established on 7 Jun 1753 when King George II gave his royal assent to an Act of Parliament on 5 Apr 1753 to acquire the collection of Sir Hans Sloane. In his will, he had offered the nation his lifetime collection of 71,000 objects, mostly plant and animal specimens. In return, he requested £20,000 for his heirs (which today would be over £2,000,000). The present museum buildings date from the mid-19th century. Its natural history collection moved to its own museum in 1881. The British Museum set up a laboratory in 1920 for its scientific studies. *TIS The myth that Sloan had invented the process of Hot Chocolate, which is still strongly promoted in the shops in Chelsea that feature this product, is a myth. See James Delbourgo's Article on Sloan and Cocoa here. Skipping to page 78 for details of the history of Chocolate in use around Europe in the 17th century.

**1827**Only once, in a book review of 1816, (this surely refers to Astral Geometry by Ferdinand Karl Schweikart ) did Gauss hint publicly at his ideas on non-Euclidean Geometry. On this date Gauss wrote his friend Schumacher that their published ideas were “besmirched with mud” by critics. *VFR It was Gauss' habit to greet new discoveries with a statement (most often without support) that he had done (whatever) years ago. PB

**1842**William Thompson (later, Lord Kelvin), at Cambridge, responds to his father's letter criticizing the inaccuracy of his accounting in his explanation of school expenses and urging his son to acquire "accurate business habits". In the letter he recommends several books to his father's library, including De Morgan's Differential Calculus, which he describes as, "very queer, but contains a great many useful ideas."* Silvanus Phillips Thompson, The Life of Lord Kelvin, Vol I

**1885**The first photo of a snowflake was taken on this day. At the age of 20, Wilson Alwyn Bentley, a farmer who would live all his life in the small town of Jericho in Vermont, gave the world its first ever photograph of a snowflake. Throughout the following winters, until his death in 1931, Bentley would go on to capture over 5000 snowflakes, or more correctly, snow crystals, on film. Despite the fact that he rarely left Jericho, thousands of Americans knew him as The Snowflake Man or simply Snowflake Bentley. Our belief that “no two snowflakes are alike” stems from a line in a 1925 report in which he remarked: “Every crystal was a masterpiece of design and no one design was ever repeated. When a snowflake melted, that design was forever lost.” *Public Domain Review

**1891**The first bimagic square (the numbers form a magic square, and when the numbers are replaced by their squares, they still form a magic square) in the world by G. Pfeffermann in France. Created in 1890, this 8x8 square was published in a french magazine "Les Tablettes du Chercheur" January 15, 1891, with only half of the numbers shown as a problem for the readers. The solution, and so the full first bimagic square, was published in the next issue of "Les Tablettes du Chercheur", February 1st 1891. Here is the original puzzle. The solution is posted on Feb 1st, as you would expect. *The Magic Encyclopedia ™ DataBase The famous Edouard Lucas (1842-1891), who was a writer of articles in Les Tablettes, wrote that this first bimagic square was a "very remarkable square". He would go on to prove that no 3x3 bimagic square could exist, even with non-consecutive digits, and that no 4x4 could be created with consecutive digits. Unfortunately he also died that same year (see link above) in as the result of a most unusual accident. 8x8 is still the smallest order bimagic square that can be formed with consecutive digits.

**1898**

**The first Annual Meeting of the Mathematical Association was held at University College, Gower Street, London, on Saturday 15 January 1898 with Alfred Lodge as President. The Report in**

*The Mathematical Gazette*states:-

There were 24 members present. The Report of the Council for 1897 was read and adopted, and the elections of 46 new members of the Association were confirmed. The Rules, which had been revised, were discussed and passed, and the Treasurer's audited financial statement was accepted. After officers and council for 1898 had been elected, a paper on "Some Curiosities in Division" was read by E M Langley, M.A., and a paper by Prof H W Lloyd Tanner on "A Class of Algebraic Functions" was, in the absence of the author, read by the President. In consequence of the lateness of the hour the other papers were postponed. *MacTutor

**1907**, the three-element vacuum tube was issued a U.S. patent to its inventor, Dr Lee de Forest as a "device for amplifying feeble electric currents - such, for example, as telephone currents" (No. 841,387). The tube was evacuated, with some remaining conducting gas molecules, and it was suggested using for the heated electrode such material as platinum, tantalum or carbon. He had made a public announcement of his device a few months earlier, on 20 Oct 1906 at a meeting of the American Institute of Electrical Engineers held in New York City. On 18 Feb 1908, he received another patent for the grid electrode tube (No. 879,532).*TIS

**1934**Artificial radioactive substances are ﬁrst produced by husband and wife Pierre and Marie Joliet-Curie. *VFR

**1941**The Des Moines Tribune pictured Clifford Berry holding part of a machine that he and John V. Atanasoff were building to solve systems of simultaneous linear equations. They expected it to contain 300 vacuum tubes when completed. [Goldstein, The Computer from Pascal to von Neumann, p. 124] *VFR (Image *Wik)

**1943**The ﬁve-story, ﬁve-sided Pentagon, the world’s largest office building with 3.7 million square feet of office space, was completed after 16 months of round-the-clock labor. *VFR

**1950**John Nash's paper, "Equilibrium Points in N-Person Games", was published in Proceedings of the National Academy of Sciences. Based on his PhD thesis, it was one page long, had two references and won its author a Nobel Prize more than 40 years later.*Ash Jogalekar

**1969**John Cocke, Michael Disney and Bob McCallister discover the ﬁrst optical pulsar. Inadvertently they tape recorded their own voices so this is perhaps the only recording of a scientific discovery as it was taking place. The whole story is available as an audio-visual package “An optical pulsar discovery.” [Center for the History of Physics Newsletter, vol. 16, no. 1, May 1984.] *VFR

**1986**The National Science Foundation opens the National Center for Supercomputer Applications (NCSA) at the University of Illinois, a national “Center of excellence” for research into high-performance computing. Its most famous alumnus, Marc Andreesen, invented his Mosaic browser for the network known as the “World Wide Web” while a student there, an effort he later transformed into the Netscape browser company. *CHM

**2001**Wikipedia was formally launched on 15 January 2001 by Jimmy Wales and Larry Sanger, using the concept and technology of a wiki pioneered in 1995 by Ward Cunningham. Initially, Wikipedia was created to complement Nupedia, an online encyclopedia project edited solely by experts, by providing additional draft articles and ideas for it. Wikipedia quickly overtook Nupedia, becoming a global project in multiple languages and inspiring a wide range of other online reference projects. *Wik

**2006**The NASA spacecraft, Stardust, used an ultralight absorbent substance called aerogel to capture more than a million particles from a comet. The materials were returned to earth in a robotic capsule that descended in a parachute in Utah, in the USA on this date. The first images of the particles were released on the 20th of January. *NASA,

**BIRTHS**

**1648 Henry Aldrich**(15 Jan 1648 in Westminster, London, England - 14 Dec 1710 in London, England) was an English theologian and philosopher.He had wide interests including mathematics, music, and architecture. He was well known as a humorist and Suttle describes him as".. a punner of the first value. "

In 1674 he published Elementa geometricae which led to him being described by his Christ Church colleagues as ".. a great mathematician of our house."

In 1691 he published Artis logicae compendium a treatise on logic which was to be the main text on the topic for 150 years in England. Even when Richard Whately published Elements of logic in 1826 it still took Aldrich's work as his starting point. *SAU

**1704 Johann Castillon**(born Giovanni Francesco Melchiore Salvemini) (January 15 1704 in Castiglione , Tuscany , October 11 1791 in Berlin ) His ﬁrst two papers dealt with the cardiod, a curve which he named in 1741. *VFR He also dealt with conic sections and quadratic equations .

Castillon published exchange of letters between Gottfried Wilhelm Leibniz and Johann Bernoulli , edited works of Leonhard Euler and published a review of Newton's Arithmetica Universalis. He also translated Locke's basic concepts of physics into French. In 1753 he became a member of the Royal Society of London. *Wik He is also known for 'Castillon's problem' which is, "To inscribe in a given circle a triangle the sides of which pass through three given points."

This problem was posed by Gabriel Cramer and solved by Castillon in 1776. *SAU

The name cardioid was first used by de Castillon in Philosophical Transactions of the Royal Society in 1741

**1717 Matthew Stewart**(15 Jan 1717 in Rothesay, Isle of Bute, Scotland - 23 Jan 1785 in Catrine, Ayrshire, Scotland)was a Scottish geometer who wrote on geometry and planetary motion. Stewart's fame is based on

*General theorems of considerable use in the higher parts of mathematics*(1746), described by John Playfair as, "... among the most beautiful, as well as most general, propositions known in the whole compass of geometry." *SAU

**1814 Ludwig Schläfli**(15 Jan 1814 in Grasswil, Bern, Switzerland - 20 March 1895 in Berne, Switzerland) Schläfli is best known for the so-called Schläfli symbols which are used to classify polyhedra. In this work, Theorie der vielfachen Kontinuität (Theory of continuous manifolds), Schläfli introduced polytopes (although he uses the word polyschemes) which he defines to be higher dimensional analogues of polygons and polyhedra. Schläfli introduced what is today called the Schläfli symbol. It is defined inductively. {n} is a regular n-gon, so {4} is a square. There {4, 3} is the cube, since it is a regular polyhedron with 3 squares {4} meeting at each vertex. Then the 4 dimensional hypercube is denoted as {4, 3, 3}, having three cubes {4, 3} meeting at each vertex. Euclid, in the Elements, proves that there are exactly five regular solids in three dimensions. Schläfli proves that there are exactly six regular solids in four dimensions {3, 3, 3}, {4, 3, 3}, {3, 3, 4}, {3, 4, 3}, {5, 3, 3}, and {3, 3, 5}, but only three in dimension n where n ≥ 5, namely {3, 3, ..., 3}, {4, 3, 3, ....,3}, and {3, 3, ...,3, 4}.

Most of Schläfli's work was in geometry, arithmetic and function theory. He gave the integral representation of the Bessel function and of the gamma function. His eight papers on Bessel functions played an important role in the preparation of G N Watson's major text Treatise on the theory of Bessel functions (1944). *SAU

**1815 Warren De la Rue**(15 Jan 1815; 19 Apr 1889) English astronomer who pioneered in astronomical photography, the method by which nearly all modern astronomical observations are made. *TIS In 1851 his attention was drawn to a daguerreotype of the Moon by G. P. Bond,(see births, 1825) shown at the great exhibition of that year. Excited to emulation and employing the more rapid wet-collodion process, he succeeded before long in obtaining exquisitely defined lunar pictures, which remained unsurpassed until the appearance of the Lewis Morris Rutherfurd photographs in 1865.

In 1854 he turned his attention to solar physics, and for the purpose of obtaining a daily photographic representation of the state of the solar surface he devised the photoheliograph, described in his report to the British Association, On Celestial Photography in England (1859), and in his Bakerian Lecture (Phil. Trans. vol. clii. pp. 333–416). Regular work with this instrument, inaugurated at Kew by De la Rue in 1858, was carried on there for fourteen years; and was continued at the Royal Observatory, Greenwich, from 1873 to 1882. *Wik

**1850 Sonya Kovalevsky**(Sofya Vasilyevna Kovalevskaya) (15 Jan 1850; 10 Feb 1891). Her bedroom was wallpapered with the pages of a text from her father’s schooldays, namely, Ostrogradsky’s lithographed lecture notes on the calculus. Study of the novel wallpaper introduced her to the calculus at age 11. She became the greatest woman mathematician prior to the twentieth century. *VFR a Russian mathematician and novelist who made valuable contributions to the theory of differential equations.*TIS

**1877 Lewis M(adison) Terman**(15 Jan 1877; 21 Dec 1956) was a U.S. psychologist who pioneered individual intelligence tests. During WW I, he was involved in mass testing of intelligence for the U.S. army. He expanded an English version of the French Binet-Simon intelligence test with which he introduced the IQ (Intelligence Quotient), being a ratio of chronological age to mental age times 100. (Thus an average child has an IQ of 100). He wrote about this metric in The Measurement of Intelligence (1916). He made a long-term study of gifted children (with IQ above 140) examining mental and physical aspect of their lives reported in the multi-volume Genetic Studies of Genius (1926-59).*TIS

**1883 James Mercer FRS**(15 January 1883 – 21 February 1932) was a mathematician, born in Bootle, close to Liverpool, England. He was educated at University of Manchester, and then University of Cambridge. He became a Fellow, saw active service at the Battle of Jutland in World War I, and after decades of suffering ill health died in London, England.

He proved Mercer's theorem, which states that positive definite kernels can be expressed as a dot product in a high-dimensional space. This theorem is the basis of the kernel trick (applied by Aizerman), which allows linear algorithms to be easily converted into non-linear algorithms. *Wik

**1900 Richard Bevan Braithwaite**(15 Jan 1900; 21 Apr 1990) was an English philosopher who trained in physics and mathematics, but turned to the philosophy of science. He examined the logical features common to all the sciences. Each science proceeds by inventing general principles from which are deduced the consequences to be tested by observation and experiment. Braithwaite was concerned with the impact of science on our beliefs about the world and the responses appropriate to that. He wrote on the statistical sciences, theories of belief and of probability, decision theory and games theory. He was interested in particular with the laws of probability as they apply to the physical and biological sciences.*TIS

**1906 G Waldo Dunnington**(January 15, 1906, Bowling Green, Missouri – April 10, 1974, Natchitoches, Louisiana) was a writer, historian and professor of German known for his writings on the famous German mathematician Carl Friedrich Gauss. Dunnington wrote several articles about Gauss and later a biography entitled Gauss: Titan of Science (ISBN 0-88385-547-X). He became interested in Gauss through one of his elementary school teachers, Minna Waldeck Gauss Reeves, who was a great-granddaughter of Gauss.

Dunnington was also a translator at the Nuremberg trials. He ended his teaching career at Northwestern State University which houses his collection of Gauss-related material, believed to be the largest collection of its kind in the world. He became Dean of International Students there near the end of his life. *Wik *The Dunnington-Gauss award is given annually at Northwestern State University to the outstanding student in mathematics.

**1908 Edward Teller**(15 Jan 1908; 9 Sep 2003) Hungarian-American nuclear physicist who participated in the production of the first atomic bomb (1945) and who led the development of the world's first thermonuclear weapon, the hydrogen bomb. After studying in Germany he left in 1933, going first to London and then to Washington, DC. He worked on the first atomic reactor, and later working on the first fission bombs during WW II at Los Alamos. Subsequently, he made a significant contribution to the development of the fusion bomb. His work led to the detonation of the first hydrogen bomb (1952). He is sometimes known as “the father of the H-bomb.” Teller's unfavourable evidence in the Robert Oppenheimer security-clearance hearing lost him some respect amongst scientists. *TIS

**1918 David George Kendall**(15 Jan 1918 in Ripon, Yorkshire, England - 23 Oct 2007 in Cambridge, England) was a leading world authority on applied probability and data analysis. *SAU

**1925 J(ames) Laurie Snell,**(January 15th, 1925, Wheaton, Illinois; March 19, 2011, Hanover, New Hampshire) was an American mathematician.

A graduate of the University of Illinois, he taught at Dartmouth College until retiring in 1995. Among his publications was the book "Introduction to Finite Mathematics", written with John George Kemeny and Gerald L. Thompson, first published in 1956 and in multiple editions since.

The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating the price process. Snell has published the related theory 1952 in the paper Applications of martingale system theorems.*Wik

**DEATHS**

**1790 John Landen**(23 Jan 1719, 15 Jan 1790) British mathematician who made important contributions on elliptic integrals. As a trained surveyor and land agent (1762-88), Landen's interest in mathematics was for leisure. He sent his results on making the differential calculus into a purely algebraic theory to the Royal Society, and also wrote on dynamics, and summation of series. Landen devised an important transformation, known by his name, giving a relation between elliptic functions which expresses a hyperbolic arc in terms of two elliptic ones. He also solved the problem of the spinning top and explained Newton's error in calculating the precession. Landen was elected a Fellow of the Royal Society in 1766. He corrected Stewart's result on the Sun-Earth distance (1771).*TIS

**1945 Wilhelm Wirtinger**(15 July 1865 – 15 January 1945) was an Austrian mathematician, working in complex analysis, geometry, algebra, number theory, Lie groups and knot theory. He worked in many areas of mathematics: according to Hornich (1948) he authored 71 works. His first significant work, published in 1896, was on theta functions. He proposed a generalization of eigenvalues, the spectrum of an operator, in an 1897 paper; the concept was extended by David Hilbert into spectral theory. Wirtinger also contributed papers on complex analysis, geometry, algebra, number theory, and Lie groups. He collaborated with Kurt Reidemeister on knot theory, showing in 1905 how to compute the knot group (fundamental group of a knot complement). Also, he was one of the editors of the Analysis section of Klein's encyclopedia.

Among his students were Wilhelm Blaschke, Leopold Vietoris, Erwin Schrödinger, Olga Taussky-Todd, and Kurt Gödel.*Wik

**1948 Henri-Alexandre Deslandres**(24 Jul 1853, 15 Jan 1948)French astrophysicist who invented a spectroheliograph (1894) to photograph the Sun in monochromatic light (about a year after George E. Hale in the U.S.) and made extensive studies of the solar chromosphere and solar activity. He worked at the Paris and Meudon Observatories. His investigation of molecular spectra produced empirical laws presaging those of quantum mechanics. He observed spectra of planets and stars and measured their radial velocities of, and he determined the rotation rates of Uranus, Jupiter and Saturn (shortly after James E. Keeler).*TIS

**1958 Aurel Friedrich Wintner**(8 April 1903 in Budapest, Hungary - 15 Jan 1958 in Baltimore, Maryland, USA) studied at Budapest and Leipzig. He spent most of his career in Johns Hopkins University in Baltimore, USA. He published on Number Theory, Differential Equations, Probability and Celestial Mechanics. Along with Poincaré and George Birkhoff, he placed celestial mechanics on a more sound mathematical basis.*SAU

**1968 Leopold Infeld**(20 Aug 1898 in Kraków, Poland - 15 Jan 1968 in Warsaw, Poland) was a Polish theoretical physicist In 1948 he published Whom the Gods Love, a biographical novel about Evariste Galois. *VFR Leopold Infeld went to England as a Fellow of the Rockefeller Foundation. In Cambridge he met Rutherford and Dirac and entered into the collaboration with Max Born, who had just arrived in England. The result of this collaboration was the Born-Infeld electrodynamics. In Princeton, Infeld collaborated with Einstein writing a popular text Evolution of Physics (1938).*SAU

**1973 Ivan Georgievich Petrovsky**(18 Jan 1901 in Sevsk, Orlov guberniya, Russia - 15 Jan 1973 in Moscow, USSR) Petrovsky's main mathematical work was on the theory of partial differential equations, the topology of algebraic curves and surfaces, and probability. Petrovsky also worked on the boundary value problem for the heat equation and this was applied to both probability theory and work of Kolmogorov.*SAU

**2007 James Hillier**, OC (August 22, 1915 – January 15, 2007) was a Canadian-born scientist and inventor who designed and built, with Albert Prebus, the first successful high-resolution electron microscope in North America in 1938. *Wik

Credits :

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*RMAT= The Renaissance Mathematicus, Thony Christie

*SAU=St Andrews Univ. Math History

*TIA = Today in Astronomy

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell

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